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Section: New Results

Exponential decay of scattering coefficients

I. Waldspurger


The scattering transform is a deep representation, defined as a cascade of wavelet transforms followed by the application of a complex modulus. In her PhD, the author showed that, under some conditions on the wavelets, the norm of the scattering coefficients at a given layer only depends on the values of the signal outside a frequency band whose size is exponential in the depth of the layer. This article succintly describes this result, and generalizes it by removing one of the assumptions on the wavelets (namely the weak analyticity condition).